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Simplifying (x + 5)(x + 1) = x(x + 1) Reorder the terms: (5 + x)(x + 1) = x(x + 1) Reorder the terms: (5 + x)(1 + x) = x(x + 1) Multiply (5 + x) * (1 + x) (5(1 + x) + x(1 + x)) = x(x + 1) ((1 * 5 + x * 5) + x(1 + x)) = x(x + 1) ((5 + 5x) + x(1 + x)) = x(x + 1) (5 + 5x + (1 * x + x * x)) = x(x + 1) (5 + 5x + (1x + x2)) = x(x + 1) Combine like terms: 5x + 1x = 6x (5 + 6x + x2) = x(x + 1) Reorder the terms: 5 + 6x + x2 = x(1 + x) 5 + 6x + x2 = (1 * x + x * x) 5 + 6x + x2 = (1x + x2) Add '-1x2' to each side of the equation. 5 + 6x + x2 + -1x2 = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 6x + 0 = 1x + x2 + -1x2 5 + 6x = 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 6x = 1x + 0 5 + 6x = 1x Solving 5 + 6x = 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 5 + 6x + -1x = 1x + -1x Combine like terms: 6x + -1x = 5x 5 + 5x = 1x + -1x Combine like terms: 1x + -1x = 0 5 + 5x = 0 Add '-5' to each side of the equation. 5 + -5 + 5x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5x = 0 + -5 5x = 0 + -5 Combine like terms: 0 + -5 = -5 5x = -5 Divide each side by '5'. x = -1 Simplifying x = -1
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